Simulations of dark energy cosmologies

Future galaxy redshift surveys will make high precision measurements of the cosmic expansion history and the growth of structure which will potentially allow us to distinguish between different scenarios for the accelerating expansion of the Universe. In this thesis we study the nonlinear growth of cosmic structure in different dark energy models, using ultra-large volume N-body simulations. We measure key observables such as the growth of large scale structure, the halo mass function and baryonic acoustic oscillations. We study the power spectrum in redshift space in $\Lambda$CDM and quintessence dark energy models and test predictions for the form of the redshift space distortions. An improved model for the redshift space power spectrum, including the non-linear velocity divergence power spectrum, is presented. We have found a density-velocity relation which is cosmology independent and which relates the non-linear velocity divergence spectrum to the non-linear matter power spectrum. We provide a formula which generates the non-linear velocity divergence $P(k)$ at any redshift, using only the non-linear matter power spectrum and the linear growth factor at the desired redshift. We also demonstrate for the first time that competing cosmological models with identical expansion histories - one with a scalar field and the other with a time-dependent change to Newton's gravitational constant - can indeed be distinguished by a measurement of the rate at which structures grow. Our calculations show that linear theory models for the power spectrum in redshift space fail to recover the correct growth rate on surprisingly large scales, leading to catastrophic systematic errors. Improved theoretical models, which have been calibrated against simulations, are needed to exploit the exquisitely accurate clustering measurements expected from future surveys

An improved model for the nonlinear velocity power spectrum

The velocity divergence power spectrum is a key ingredient in modelling redshift space distortion effects on quasi-linear and nonlinear scales. We present an improved model for the z=0 velocity divergence auto and cross power spectrum which was originally suggested by Jennings et al. 2011. Using numerical simulations we measure the velocity fields using a Delaunay tesselation and obtain an accurate prediction of the velocity divergence power spectrum on scales k < 1 hMpc^{-1}. We use this to update the model which is now accurate to 2% for both P_{\theta \theta} and P_{\theta \delta} at z=0 on scales k <0.7 hMpc^{-1} and k <0.5 hMpc^{-1} respectively. We find that the formula for the redshift dependence of the velocity divergence power spectra proposed by Jennings et al. 2011 recovers the measured z>0 P(k) to markedly greater accuracy with the new model. The nonlinear P_{\theta \theta} and P_{\theta \delta} at z =1 are recovered accurately to better than 2% on scales k<0.2 hMpc^{-1}. Recently it was shown that the velocity field shows larger differences between modified gravity cosmologies and \Lambda CDM compared to the matter field. An accurate model for the velocity divergence power spectrum, such as the one presented here, is a valuable tool for analysing redshift space distortion effects in future galaxy surveys and for constraining deviations from general relativity.Comment: 5 pages, 2 figures, Accepted for publication in MNRA